- Email: [email protected]
Lamellar spacing selection in a directionally solidified SnSe eutectic alloy
j. . . . . . . .
CRYSTAL G R O W T H
Journal of Crystal Growth 174 (1997) 70-75
ELSEVIER
a
Lamellar spacing selection in directionally solidified Sn-Se eutectic alloy M.R. Aguiar, R. Caram* State University of Campinas, P.O. Box 6122, Campinas, SP, 13083-970, CP 6122, Brazil
Abstract According to the classical eutectic growth theory, eutectic solidification occurs near the minimum liquid undercooling at the solid/liquid interface. Application of such a condition on eutectic solidification leads to the conclusion that the lamellar spacing is not unique for a specific growth condition. Although the average lamellar spacing as a function of the growth rate agrees with the theory, in the growth of the Sn-Se eutectic alloy, it was found that the lamellar spacings are distributed over a large range of values. The main objective of this paper is to investigate the influence of the growth rate on the lamellar spacing selection of the Sn-Se eutectic alloy. The results obtained show that the growth rate affects the distribution of lamellar spacings. It was noted that an increase in the growth rate causes a narrower distribution of spacings. Keywords: Eutectic growth; Directional solidification
1. Introduction In recent years directional solidification of eutectic alloys has been the topic of a n u m b e r of theoretical and experimental investigations. The p r i m a r y motivating factor in carrying out these studies has been the possibility of producing composite materials directly from the melt, also described as in situ composites.
*Corresponding author. Fax: + 55 192 393722; e-mail: [email protected].
W h e n a eutectic alloy is directionally solidified, occasionally, a regular structure consisting of two coexisting solid phases is formed: the ~ and 13 phases. In this case, the solidification process leads to cooperative growth of oriented and anisotropic structure, where both solid phases grow side by side. The cooperative growth of an eutectic alloy is mainly a function of simultaneous diffusion ahead of the growth interface. While the ~ phase segregates the constituent B, the 13 phase rejects the constituent A. Such a p h e n o m e n o n leads to a solute build up in the liquid in front of the ~ and 13phases and hence, to lateral solute diffusion of A and B.
0022-0248/97/$17.00 Copyright iS' 1997 Elsevier Science B.V. All rights reserved PII S 0 0 2 2 - 0 2 4 8 ( 9 6 ) 0 1 0 6 2 - 7
M.R. Aguiar, R. Caram ,/Journal o/'Crystal Growth 174 (1997) 70 75
Lateral diffusion is essential to proceeding with the eutectic growth process. Eutectic growth has been examined in a number of investigations [1-5]. The basis of the eutectic growth theory was obtained from the Zener model of the eutectoid transformation [6]. Zener pointed out that the product of the growth rate and the square of the lamellar spacing should be constant. In their classic work, Jackson and Hunt [7] developed a quantitative theory of the regular lamellar eutectic growth based on a solution for the diffusion problem at the solid/liquid interface. Considering that the 2 and 13phase interfaces are plane, they developed a relationship between the total interface undercooling, the solute concentration field and the interface curvature (neglecting the kinetic undercooling). The undercooling due to the composition deviation from eutectic composition, which is a result of the diffusion in liquid adjacent to the interface, is obtained from the phase diagram. The undercooling caused by the curvature at the solid/liquid interface is related to the GibbsThomson equation. The total undercooling, A T , of the solidifying interface as a function of both the growth rate, V, and the lamellar spacing, 2, is calculated by the equation: K~
A T = K t 2 V + -:-:,
(1)
A
[., g:
°~
0 0 k~
e~ Unstable
Stable
71
where K1 and K2 can be evaluated from the phase diagram and from thermodynamic data. The relationship between lamellar spacing and the interface undercooling at a constant growth rate is given in Fig. 1. Based on the Zener [6] and Tiller [8] investigations, Jackson and Hunt assumed that the eutectic growth occurs near the 'extremum condition', which is associated with the minimum liquid undercooling at solid/liquid interface or with the maximum growth rate. Application of such a principle produces the following relationship between AT, 2 and V: ;.~x,v = - : - .
K1
I2)
According to the Jackson and Hunt theory [7], lamellar spacings smaller than the extremum spacing, ),ex, are unstable, while lamellar spacings larger than the extremum lamellar spacing are stable with respect to fluctuations in the solid/liquid interface. The maximum spacing, 2 .... is limited by the motion of lamellar faults. Consequently, the eutectic growth at constant growth rate occurs within a small range of spacing values, near the extremum spacing. Utilization of such a theory on eutectic solidification leads to the conclusion that the lamellar interspacing value is not unique for a particular growth condition. With regard to the directional solidification of a Sn--Se eutectic alloy, an interesting observation was made. Using a constant growth rate, it was found that the lamellar spacings are distributed in a very extensive range of values. Such an occurrence shows that the lamellar spacing selection is not narrow and a finite dispersion of spacing values is found for a specific growth rate. The main aim of this study was to analyze experimentally the influence of the growth rate on the lamellar spacing selection of the Sn Se eutectic alloy.
Unstable
2. Experimental details ~Lext.
~max.
Lamellar Spacing, Fig. 1. U n d e r c o o l i n g as a function of the l a m e l l a r s p a c i n g at a c o n s t a n t g r o w t h rate.
The objective of the experiments was to determine the influence of the growth tale on the SnSe-SnSe2 eutectic microstructure of a directionally solidified sample. In order to obtain directional
72
M.R. Aguiar, R. Caram / Journal of Crystal Growth 174 (1997) 70-75
solidification, a vertical Bridgman-Stockbarger crystal growth unit was utilized. The vertical Bridgman-Stockbarger method basically consists of slowly moving an ampoule containing the growth material from a hot zone (high temperature) into a cold zone (low temperature), By using such a procedure it is possible to manipulate the temperature gradient at solid/liquid interface, the growth rate and the shape of the growth interface. The hot zone at the top and the cold zone below were made up of two transparent gold-deposited heating units and separated by insulation. The heating elements were obtained from sheathed coax as a rigid coil. Alloys were prepared by weighing a proper amount of 99.99% pure Se pellets supplied by the Aldrich Chemical Company, Inc. and 99.999% pure Sn shot supplied by Johnson Matthey Chemicals Limited, corresponding to 50.96wt% Se. Quartz tubes were sealed at one end and utilized as the material for encapsulating the growth alloy. Quartz ampoules containing the Sn-Se alloy were purged with an inert gas (argon) and sealed under vacuum of 10- 5 Torr, The quartz tubes were 0.8 cm ID x 1.0 cm O D and 55.0 cm long. In order to obtain very regular eutectic growth, it was necessary to achieve well-homogenized alloys before carrying out the directional solidification. Homogenization was obtained by processing the growth material in a rocking furnace at 860°C for 4 h. The quartz ampoules containing the Sn-Se homogenized alloy were transferred to the crystal growth apparatus for directional solidification experiments. Ingots 6.0 cm in length and 0.8 cm in diameter were grown by pulling down the ampoule from the hot to cold zone at lowering rates ranging from 0.473.07 cm/h. All of the directional solidification experiments were carried out with the same hot and cold zone temperatures. The hot zone was set at a temperature of 850°C, while the cold zone was set at 150°C. The effect of the growth rate on the microstructure was found by taking cross-section samples at several locations along the ingot. The cut sections were mounted with wax on a brass matrix. First the specimen was mechanically polished and then, chemically, in a solution of 100 ml of absolute ethanol and 2 g of iodine. The microstructure morphology analysis as well as the interphase spacing measurements for these samples
were determined using an optical microscope. On each section, the length of about one hundred lamellae pairs was measured in a normal direction to the growth direction. Since the SnSe and SnSe2 lamellas were extremely small, a scanning electron microscope was also employed to observe the lamellar structure. Longitudinal samples were also analyzed using optical and scanning electron microscopes.
3. Results and discussion According to several experimental investigations on regular eutectic growth, the lamellar spacing is scattered within a finite band of width at a given growth rate [9-1 l]. In the directional solidification eutectic system composed by the phases SnSe and SnSe2, the range of spacings was found to be considerable. Such a result was also observed by Shinohara et al. [-12]. Fig. 2 shows the longitudinal and radial micrographs of the specimens obtained at V = 0.47 cm/h. Both views show that the lamellar spacing is not unique. In order to establish the effect of the growth rate on the lamellar microstructure, samples were grown at varying growth rates of 0.47 3.07 cm/h. The effect of the growth rate on the average lamellar spacings was measured in several binary systems and, generally, the experimental results follow Eq. (2) [13]. Fig. 3 presents the variation in average lamellar spacing with the growth rate obtained from the directionally solidified Sn-Se eutectic alloy samples. This figure shows that an increase in the growth rate produces a decrease in the spacing values. The effect of the growth rate on lamellar spacing follows the classic relationship V22 = constant. The constant in Eq. (2) was found to be 5.0x 10 -s cm3/h. In the present study, the use of different values of growth rate did not result in the cessation of the regular growth. In all the growth conditions employed, the microstructure remained lamellar, even though the lamellae pairs did not show the same value, but a range of values. The range of spacing was very wide, since at a given growth rate, spacing values ranging from 50% to 150% of the average value were measured. Such behavior is not usually found in eutectic investigations.
73
M.R. Aguiar, R. Caram / Journal Ol'Oystal Growth 174 (1997) 70 75
3.0 A
Experimental Results
::L
.=.
2.0-
.l t_
.< 1,0
0.5
0.7
0.9
I.I
1.3
1.5
(Growth Rate, cm/hr)"1/2
Fig. 3. Lamellarspacing as a funclion of the inverse square root of the growth rate.
Fig. 2. lmmellar Sn Sc eutectic microstructure grown [' = 0.47 m h : (a} longitudinal view and (b) radial view.
al
The use of different growth conditions showed that the distributions of the lamellar spacings appeared to be a function of the growth rate. To understand such behavior, an analysis of the frequency distributions of the spacings was conducted. Fig. 4 shows the frequency distributions of the lamellar spacings obtained at several growth rates. To easily compare the results obtained under different growth conditions, the abscissa was normalized and plotted as 2/2 ....... as done before by Seetharaman and Trivedi [14]. For the lowest growth rate. V = 0.47 cm/h (Fig. 4a), the frequency distribution shows that the spacing values are scattered in a very wide band of values which ranged from 0.6,;....... to 1.5)........ where the average lamellar spacing, 2 ....... was found to be 2.7 lam. At such
a growth rate. the maximum frequency was 15"/o. At V = 1.54cm/h, the frequency distribution (Fig. 4b) is still very large but smaller than the first case. The spacings ranged again from 0.62 ...... to 1.5)........ the average spacing was 1.9 btm and the maximum frequency of 18°A, was obtained. At V = 2.03 cm/h (Fig. 4c}, the spacing variation is smaller than the other cases since the experimental observation resulted in lamellar spacings of 0.7,:~....... to 1.52....... an average spacing of 1.6 [am, and the maximum frequency was 26.5%. Finally, at V - 3.07 cm/h, the distribution of the lamellar spacings is very narrow compared to the results obtained at smaller growth rates. While the spacings were distributed within a range of 0.62 ...... to 1.4Z........ the average spacing value was 1.2 [am, and a maximum frequency of 30% was determined. These results clearly show that the frequency distribution of the lamellar spacings is a function of the growth rate. Such a behavior was already observed by Seetharam and Trivedi [14] in the study of selection of lamellar spacing during the directional solidification of the carbon tetrabromide (CBr4)hexachloroethane (C2C16) system. However, the lamellar spacings obtained in Seetharam and
A/LR. Aguiar, R. Caram / Journal of Crystal Growth 174 (1997) 70- 75
74
30
30
V=0.47cm/hr
V=l.54cm/hr
25
25-
~, 20
,~ 20A /',
-~ 15-
A
A A A
A
~. 10
~-
AAA
A A
A A A
|
|
A
A
I
!
!
A
I
A i
1.0
0.5
(a)
A
AAA [
A
A
A
A
10-
A
1.5
Relative Lamellar Spacing, M~ aver.
(b)
30
i
i
[
[
A
i
[
1.5
1.0 Relative Lamellar Spacing, ~/~-aver.
0.5
A
30 V=2.03cm/h
25-
i
V=3.07cm/h
A
25
A --, 2 0 -~ q~
20 A
15-
A
g
A
10-
A
k. 10
A
A A
,
0.5 (c)
,
,
,
I
'
'
'
A
A
,
1.0 1.5 Relative Lamellar Spacing, ~/~aver.
I
0.5 (d)
I
[
I
I
I
I
I
I
1.0 1.5 Relative Lamellar Spacing, ~J~aver.
Fig. 4. F r e q u e n c y d i s t r i b u t i o n s of the l a m e l l a r spacings o b t a i n e d at different g r o w t h rates: (a) 0.47; (b) 1.54; (c) 2.03 and (d) 3.07 cm/h.
Trivedi's investigation were distributed within a m a x i m u m range of 0.82 to 1.42 which is narrower than the results observed in the present investigation. A reasonable hypothesis for the very wide frequency distributions for the SnSe-SnSe2 eutectic microstructure involves the growth characteristics of the individual constituent phases [15]. These ....
.
....
.,
characteristics are related to the nature of the solid/liquid interface, which is controlled by the entropy of fusion value [16]. Thus, the behavior of the SnSe and SnSe2 compounds during their solidification can be estimated by finding their latent heats of fusion. The latent heats of fusion of the SnSe and SnS% were measured using a DSC equipment. The entropies of fusion of the SnSe and SnSe2
M.R. Aguiar. R. Caram / Journal o[ Cr),stal Growth 174 (1997) 70 75
compounds were estimated to be close to 25 and 71 J/mol. K, respectively. Although SnSe-SnSe2 eutectic microstructure is very regular, the entropy of both compounds were found to be high compared with non-faceted materials [15, 16], which indicates that faceted behavior would be expected. According to Podolinsky et al. [17], in solutions, a faceted component can become non-faceted and vice versa, as a result of the influence of the second component. In spite of that, the high values of entropy of fusion could be related to the broad distributions in the lamellar spacings, since the difficulty in branching produces spacings with several values for a constant growth rate.
75
fusion of the SnSe and SnSe2 compounds resulted in high values for both phases, the use of different growth conditions did not interrupt the regular growth. In all the growth conditions employed, the microstructure remained lamellar.
Acknowledgements The authors would like to thank CNPq, FAPESP and FAEP-UNICAMP for their financial support.
References 4. Conclusions Directional growth experiments were carried out with the Sn-Se eutectic alloy, and the effect of the growth rate on the distribution of lamellar spacing was investigated. Based on the results obtained, it can be affirmed that the effect of the growth rate on the eutectic microstructure is in good concordance with the theory, i.e., the lamellar spacing is proportional to the inverse of the square root of the growth rate. As predicted by the Jackson and Hunt theory [7], the experimental results show that lamellar spacings are scattered over a finite range of values. The experimental results also show that the growth rate influences the frequency distribution of the lamellar spacing at a constant growth freezing. An increase in the growth rate decreases the spread in lamellar spacings, represented by the difference between the maximum and minimum values of 2/)~..... . Although an evaluation of the entropy of
[1] [2] [3] [4]
J. Liu, Z. Liu and Z. Wu, Mater. Sci. Eng. A 167 (1993) 87. J. Liu and R. Ellion, Met. Mater. Trans. A 26 (1995) 471. J. Liu and R. Ellion, J. Crystal Growth 148 (1995) 406. R. Caram, S. Chandrasekhar and W.R. Wilcox, J. Crystal Growth 106 (1990) 294. [5] W. Kurz and R. Trivedi, Met. Trans. A 22 (1991) 3051. [6] C. Zener, Trans. AIME 167 (1946) 550. [7] K.A. Jackson and J.D. Hunt, Trans. AIME 236 (1966) 1129.
[8] W.A. Tiller, in: Liquid Metals and Solidification (ASM, Metals Park, OH, 1958) p. 276. [9] J.N. Clark and R. Elliott, Met. Trans. A 7 (19761 1197. [10] R. TrivedL J.T. Mason, J.D. Verhoeven and W. Kurz. Met. Trans. A 22 (1991) 2523. [11] R.M. Jordan and J.D. Hunt, Met. Trans. 2 (1971) 3401. [12] K. Shinohara, T. Seo and S. Isomura, S~dhamfi 11 (1987) 397. [13] W. Kurz and D.J. Fisher, Int. Met. Rev. 24 (1979) 177. [14] V. Seethararnan and R. Trivedi, Met. Trans. A 19 119881 2955. [15] R. Elliott, Int. Met. Rev. 22 (1977) 161. [16] K.A. Jackson, in: Liquid Metals and Solidification (ASM, Metals Park, OH, 1958) p. 174. [17] V.V. Podolinsky, Y.N. Taran and V.G. Drykin, J. Crystal Growth 96 {1989) 445.
CRYSTAL G R O W T H
Journal of Crystal Growth 174 (1997) 70-75
ELSEVIER
a
Lamellar spacing selection in directionally solidified Sn-Se eutectic alloy M.R. Aguiar, R. Caram* State University of Campinas, P.O. Box 6122, Campinas, SP, 13083-970, CP 6122, Brazil
Abstract According to the classical eutectic growth theory, eutectic solidification occurs near the minimum liquid undercooling at the solid/liquid interface. Application of such a condition on eutectic solidification leads to the conclusion that the lamellar spacing is not unique for a specific growth condition. Although the average lamellar spacing as a function of the growth rate agrees with the theory, in the growth of the Sn-Se eutectic alloy, it was found that the lamellar spacings are distributed over a large range of values. The main objective of this paper is to investigate the influence of the growth rate on the lamellar spacing selection of the Sn-Se eutectic alloy. The results obtained show that the growth rate affects the distribution of lamellar spacings. It was noted that an increase in the growth rate causes a narrower distribution of spacings. Keywords: Eutectic growth; Directional solidification
1. Introduction In recent years directional solidification of eutectic alloys has been the topic of a n u m b e r of theoretical and experimental investigations. The p r i m a r y motivating factor in carrying out these studies has been the possibility of producing composite materials directly from the melt, also described as in situ composites.
*Corresponding author. Fax: + 55 192 393722; e-mail: [email protected].
W h e n a eutectic alloy is directionally solidified, occasionally, a regular structure consisting of two coexisting solid phases is formed: the ~ and 13 phases. In this case, the solidification process leads to cooperative growth of oriented and anisotropic structure, where both solid phases grow side by side. The cooperative growth of an eutectic alloy is mainly a function of simultaneous diffusion ahead of the growth interface. While the ~ phase segregates the constituent B, the 13 phase rejects the constituent A. Such a p h e n o m e n o n leads to a solute build up in the liquid in front of the ~ and 13phases and hence, to lateral solute diffusion of A and B.
0022-0248/97/$17.00 Copyright iS' 1997 Elsevier Science B.V. All rights reserved PII S 0 0 2 2 - 0 2 4 8 ( 9 6 ) 0 1 0 6 2 - 7
M.R. Aguiar, R. Caram ,/Journal o/'Crystal Growth 174 (1997) 70 75
Lateral diffusion is essential to proceeding with the eutectic growth process. Eutectic growth has been examined in a number of investigations [1-5]. The basis of the eutectic growth theory was obtained from the Zener model of the eutectoid transformation [6]. Zener pointed out that the product of the growth rate and the square of the lamellar spacing should be constant. In their classic work, Jackson and Hunt [7] developed a quantitative theory of the regular lamellar eutectic growth based on a solution for the diffusion problem at the solid/liquid interface. Considering that the 2 and 13phase interfaces are plane, they developed a relationship between the total interface undercooling, the solute concentration field and the interface curvature (neglecting the kinetic undercooling). The undercooling due to the composition deviation from eutectic composition, which is a result of the diffusion in liquid adjacent to the interface, is obtained from the phase diagram. The undercooling caused by the curvature at the solid/liquid interface is related to the GibbsThomson equation. The total undercooling, A T , of the solidifying interface as a function of both the growth rate, V, and the lamellar spacing, 2, is calculated by the equation: K~
A T = K t 2 V + -:-:,
(1)
A
[., g:
°~
0 0 k~
e~ Unstable
Stable
71
where K1 and K2 can be evaluated from the phase diagram and from thermodynamic data. The relationship between lamellar spacing and the interface undercooling at a constant growth rate is given in Fig. 1. Based on the Zener [6] and Tiller [8] investigations, Jackson and Hunt assumed that the eutectic growth occurs near the 'extremum condition', which is associated with the minimum liquid undercooling at solid/liquid interface or with the maximum growth rate. Application of such a principle produces the following relationship between AT, 2 and V: ;.~x,v = - : - .
K1
I2)
According to the Jackson and Hunt theory [7], lamellar spacings smaller than the extremum spacing, ),ex, are unstable, while lamellar spacings larger than the extremum lamellar spacing are stable with respect to fluctuations in the solid/liquid interface. The maximum spacing, 2 .... is limited by the motion of lamellar faults. Consequently, the eutectic growth at constant growth rate occurs within a small range of spacing values, near the extremum spacing. Utilization of such a theory on eutectic solidification leads to the conclusion that the lamellar interspacing value is not unique for a particular growth condition. With regard to the directional solidification of a Sn--Se eutectic alloy, an interesting observation was made. Using a constant growth rate, it was found that the lamellar spacings are distributed in a very extensive range of values. Such an occurrence shows that the lamellar spacing selection is not narrow and a finite dispersion of spacing values is found for a specific growth rate. The main aim of this study was to analyze experimentally the influence of the growth rate on the lamellar spacing selection of the Sn Se eutectic alloy.
Unstable
2. Experimental details ~Lext.
~max.
Lamellar Spacing, Fig. 1. U n d e r c o o l i n g as a function of the l a m e l l a r s p a c i n g at a c o n s t a n t g r o w t h rate.
The objective of the experiments was to determine the influence of the growth tale on the SnSe-SnSe2 eutectic microstructure of a directionally solidified sample. In order to obtain directional
72
M.R. Aguiar, R. Caram / Journal of Crystal Growth 174 (1997) 70-75
solidification, a vertical Bridgman-Stockbarger crystal growth unit was utilized. The vertical Bridgman-Stockbarger method basically consists of slowly moving an ampoule containing the growth material from a hot zone (high temperature) into a cold zone (low temperature), By using such a procedure it is possible to manipulate the temperature gradient at solid/liquid interface, the growth rate and the shape of the growth interface. The hot zone at the top and the cold zone below were made up of two transparent gold-deposited heating units and separated by insulation. The heating elements were obtained from sheathed coax as a rigid coil. Alloys were prepared by weighing a proper amount of 99.99% pure Se pellets supplied by the Aldrich Chemical Company, Inc. and 99.999% pure Sn shot supplied by Johnson Matthey Chemicals Limited, corresponding to 50.96wt% Se. Quartz tubes were sealed at one end and utilized as the material for encapsulating the growth alloy. Quartz ampoules containing the Sn-Se alloy were purged with an inert gas (argon) and sealed under vacuum of 10- 5 Torr, The quartz tubes were 0.8 cm ID x 1.0 cm O D and 55.0 cm long. In order to obtain very regular eutectic growth, it was necessary to achieve well-homogenized alloys before carrying out the directional solidification. Homogenization was obtained by processing the growth material in a rocking furnace at 860°C for 4 h. The quartz ampoules containing the Sn-Se homogenized alloy were transferred to the crystal growth apparatus for directional solidification experiments. Ingots 6.0 cm in length and 0.8 cm in diameter were grown by pulling down the ampoule from the hot to cold zone at lowering rates ranging from 0.473.07 cm/h. All of the directional solidification experiments were carried out with the same hot and cold zone temperatures. The hot zone was set at a temperature of 850°C, while the cold zone was set at 150°C. The effect of the growth rate on the microstructure was found by taking cross-section samples at several locations along the ingot. The cut sections were mounted with wax on a brass matrix. First the specimen was mechanically polished and then, chemically, in a solution of 100 ml of absolute ethanol and 2 g of iodine. The microstructure morphology analysis as well as the interphase spacing measurements for these samples
were determined using an optical microscope. On each section, the length of about one hundred lamellae pairs was measured in a normal direction to the growth direction. Since the SnSe and SnSe2 lamellas were extremely small, a scanning electron microscope was also employed to observe the lamellar structure. Longitudinal samples were also analyzed using optical and scanning electron microscopes.
3. Results and discussion According to several experimental investigations on regular eutectic growth, the lamellar spacing is scattered within a finite band of width at a given growth rate [9-1 l]. In the directional solidification eutectic system composed by the phases SnSe and SnSe2, the range of spacings was found to be considerable. Such a result was also observed by Shinohara et al. [-12]. Fig. 2 shows the longitudinal and radial micrographs of the specimens obtained at V = 0.47 cm/h. Both views show that the lamellar spacing is not unique. In order to establish the effect of the growth rate on the lamellar microstructure, samples were grown at varying growth rates of 0.47 3.07 cm/h. The effect of the growth rate on the average lamellar spacings was measured in several binary systems and, generally, the experimental results follow Eq. (2) [13]. Fig. 3 presents the variation in average lamellar spacing with the growth rate obtained from the directionally solidified Sn-Se eutectic alloy samples. This figure shows that an increase in the growth rate produces a decrease in the spacing values. The effect of the growth rate on lamellar spacing follows the classic relationship V22 = constant. The constant in Eq. (2) was found to be 5.0x 10 -s cm3/h. In the present study, the use of different values of growth rate did not result in the cessation of the regular growth. In all the growth conditions employed, the microstructure remained lamellar, even though the lamellae pairs did not show the same value, but a range of values. The range of spacing was very wide, since at a given growth rate, spacing values ranging from 50% to 150% of the average value were measured. Such behavior is not usually found in eutectic investigations.
73
M.R. Aguiar, R. Caram / Journal Ol'Oystal Growth 174 (1997) 70 75
3.0 A
Experimental Results
::L
.=.
2.0-
.l t_
.< 1,0
0.5
0.7
0.9
I.I
1.3
1.5
(Growth Rate, cm/hr)"1/2
Fig. 3. Lamellarspacing as a funclion of the inverse square root of the growth rate.
Fig. 2. lmmellar Sn Sc eutectic microstructure grown [' = 0.47 m h : (a} longitudinal view and (b) radial view.
al
The use of different growth conditions showed that the distributions of the lamellar spacings appeared to be a function of the growth rate. To understand such behavior, an analysis of the frequency distributions of the spacings was conducted. Fig. 4 shows the frequency distributions of the lamellar spacings obtained at several growth rates. To easily compare the results obtained under different growth conditions, the abscissa was normalized and plotted as 2/2 ....... as done before by Seetharaman and Trivedi [14]. For the lowest growth rate. V = 0.47 cm/h (Fig. 4a), the frequency distribution shows that the spacing values are scattered in a very wide band of values which ranged from 0.6,;....... to 1.5)........ where the average lamellar spacing, 2 ....... was found to be 2.7 lam. At such
a growth rate. the maximum frequency was 15"/o. At V = 1.54cm/h, the frequency distribution (Fig. 4b) is still very large but smaller than the first case. The spacings ranged again from 0.62 ...... to 1.5)........ the average spacing was 1.9 btm and the maximum frequency of 18°A, was obtained. At V = 2.03 cm/h (Fig. 4c}, the spacing variation is smaller than the other cases since the experimental observation resulted in lamellar spacings of 0.7,:~....... to 1.52....... an average spacing of 1.6 [am, and the maximum frequency was 26.5%. Finally, at V - 3.07 cm/h, the distribution of the lamellar spacings is very narrow compared to the results obtained at smaller growth rates. While the spacings were distributed within a range of 0.62 ...... to 1.4Z........ the average spacing value was 1.2 [am, and a maximum frequency of 30% was determined. These results clearly show that the frequency distribution of the lamellar spacings is a function of the growth rate. Such a behavior was already observed by Seetharam and Trivedi [14] in the study of selection of lamellar spacing during the directional solidification of the carbon tetrabromide (CBr4)hexachloroethane (C2C16) system. However, the lamellar spacings obtained in Seetharam and
A/LR. Aguiar, R. Caram / Journal of Crystal Growth 174 (1997) 70- 75
74
30
30
V=0.47cm/hr
V=l.54cm/hr
25
25-
~, 20
,~ 20A /',
-~ 15-
A
A A A
A
~. 10
~-
AAA
A A
A A A
|
|
A
A
I
!
!
A
I
A i
1.0
0.5
(a)
A
AAA [
A
A
A
A
10-
A
1.5
Relative Lamellar Spacing, M~ aver.
(b)
30
i
i
[
[
A
i
[
1.5
1.0 Relative Lamellar Spacing, ~/~-aver.
0.5
A
30 V=2.03cm/h
25-
i
V=3.07cm/h
A
25
A --, 2 0 -~ q~
20 A
15-
A
g
A
10-
A
k. 10
A
A A
,
0.5 (c)
,
,
,
I
'
'
'
A
A
,
1.0 1.5 Relative Lamellar Spacing, ~/~aver.
I
0.5 (d)
I
[
I
I
I
I
I
I
1.0 1.5 Relative Lamellar Spacing, ~J~aver.
Fig. 4. F r e q u e n c y d i s t r i b u t i o n s of the l a m e l l a r spacings o b t a i n e d at different g r o w t h rates: (a) 0.47; (b) 1.54; (c) 2.03 and (d) 3.07 cm/h.
Trivedi's investigation were distributed within a m a x i m u m range of 0.82 to 1.42 which is narrower than the results observed in the present investigation. A reasonable hypothesis for the very wide frequency distributions for the SnSe-SnSe2 eutectic microstructure involves the growth characteristics of the individual constituent phases [15]. These ....
.
....
.,
characteristics are related to the nature of the solid/liquid interface, which is controlled by the entropy of fusion value [16]. Thus, the behavior of the SnSe and SnSe2 compounds during their solidification can be estimated by finding their latent heats of fusion. The latent heats of fusion of the SnSe and SnS% were measured using a DSC equipment. The entropies of fusion of the SnSe and SnSe2
M.R. Aguiar. R. Caram / Journal o[ Cr),stal Growth 174 (1997) 70 75
compounds were estimated to be close to 25 and 71 J/mol. K, respectively. Although SnSe-SnSe2 eutectic microstructure is very regular, the entropy of both compounds were found to be high compared with non-faceted materials [15, 16], which indicates that faceted behavior would be expected. According to Podolinsky et al. [17], in solutions, a faceted component can become non-faceted and vice versa, as a result of the influence of the second component. In spite of that, the high values of entropy of fusion could be related to the broad distributions in the lamellar spacings, since the difficulty in branching produces spacings with several values for a constant growth rate.
75
fusion of the SnSe and SnSe2 compounds resulted in high values for both phases, the use of different growth conditions did not interrupt the regular growth. In all the growth conditions employed, the microstructure remained lamellar.
Acknowledgements The authors would like to thank CNPq, FAPESP and FAEP-UNICAMP for their financial support.
References 4. Conclusions Directional growth experiments were carried out with the Sn-Se eutectic alloy, and the effect of the growth rate on the distribution of lamellar spacing was investigated. Based on the results obtained, it can be affirmed that the effect of the growth rate on the eutectic microstructure is in good concordance with the theory, i.e., the lamellar spacing is proportional to the inverse of the square root of the growth rate. As predicted by the Jackson and Hunt theory [7], the experimental results show that lamellar spacings are scattered over a finite range of values. The experimental results also show that the growth rate influences the frequency distribution of the lamellar spacing at a constant growth freezing. An increase in the growth rate decreases the spread in lamellar spacings, represented by the difference between the maximum and minimum values of 2/)~..... . Although an evaluation of the entropy of
[1] [2] [3] [4]
J. Liu, Z. Liu and Z. Wu, Mater. Sci. Eng. A 167 (1993) 87. J. Liu and R. Ellion, Met. Mater. Trans. A 26 (1995) 471. J. Liu and R. Ellion, J. Crystal Growth 148 (1995) 406. R. Caram, S. Chandrasekhar and W.R. Wilcox, J. Crystal Growth 106 (1990) 294. [5] W. Kurz and R. Trivedi, Met. Trans. A 22 (1991) 3051. [6] C. Zener, Trans. AIME 167 (1946) 550. [7] K.A. Jackson and J.D. Hunt, Trans. AIME 236 (1966) 1129.
[8] W.A. Tiller, in: Liquid Metals and Solidification (ASM, Metals Park, OH, 1958) p. 276. [9] J.N. Clark and R. Elliott, Met. Trans. A 7 (19761 1197. [10] R. TrivedL J.T. Mason, J.D. Verhoeven and W. Kurz. Met. Trans. A 22 (1991) 2523. [11] R.M. Jordan and J.D. Hunt, Met. Trans. 2 (1971) 3401. [12] K. Shinohara, T. Seo and S. Isomura, S~dhamfi 11 (1987) 397. [13] W. Kurz and D.J. Fisher, Int. Met. Rev. 24 (1979) 177. [14] V. Seethararnan and R. Trivedi, Met. Trans. A 19 119881 2955. [15] R. Elliott, Int. Met. Rev. 22 (1977) 161. [16] K.A. Jackson, in: Liquid Metals and Solidification (ASM, Metals Park, OH, 1958) p. 174. [17] V.V. Podolinsky, Y.N. Taran and V.G. Drykin, J. Crystal Growth 96 {1989) 445.